Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

The effect of quadrature on the dynamics of a discretised nonlinear integro-differential equation

Aves, M.A. and Davies, P.J. and Higham, D.J. (2000) The effect of quadrature on the dynamics of a discretised nonlinear integro-differential equation. Applied Numerical Mathematics, 32 (1). pp. 1-20. ISSN 0168-9274

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

The long-term dynamics of a discretized, nonlinear, integro-differential equation with convolution kernel are studied. For a constant time-step algorithm the existence and stability of fixed and periodic points are investigated. A systematic treatment is given, which quantifies the effect of varying the quadrature rule and integrating the kernel exactly or approximately. Special attention is paid to spurious behaviour that occurs below, or around, the 'natural' time-step that corresponds to the linear stability limit for the correct fixed point. It is shown that spurious solutions exist, and can be computed, within this linear stability range. In addition to fixed points and period two solutions, analysis is performed for a class of period three orbits that are observed to be relevant to the long-term dynamics. Finally, an adaptive algorithm, based on local error control, is studied and a simple model describing its long-term behaviour is developed.